A sum of money doubles itself on simple interest in 10 years. Find the rate of interest per annum.

Let the principal be \( P \).

Since the money doubles in 10 years, the total amount becomes \( 2P \).
So, Simple Interest (SI) = \( 2P - P = P \)

Use the formula:
$$\text{SI} = \frac{P \cdot R \cdot T}{100}$$ Substituting values: $$P = \frac{P \cdot R \cdot 10}{100}$$ Cancel \( P \) on both sides: $$1 = \frac{R \cdot 10}{100} \Rightarrow R = \frac{100}{10} = \boxed{10\%}$$
Final Answer:
$$\boxed{10\% \text{ per annum}}$$